anonymous
  • anonymous
limit of (5x+2)/sqrt(9x^2+3x+1)-x as x approaches -infinity
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+3 x+1}-x},x\to \text{Infinity}\right]=\frac{5}{2} \]
anonymous
  • anonymous
rob its approaching negative infinity
anonymous
  • anonymous
also can you please demonstrate in steps. i need to understand how to to dow this. and the denominator is actually sqrt(9x^2+x-3) sorry

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anonymous
  • anonymous
crap let me rewrite the question... i made alot of mistakes
anonymous
  • anonymous
\[\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}\]
anonymous
  • anonymous
Sorry. missed the -infinity requirement.\[\text{Limit}\left[\frac{5 x+2}{\sqrt{9 x^2+ x-3}},x\to -\text{Infinity}\right]=-\frac{5}{3}=1.6667 \]A plot of the problem expression from -100 throught zero is attached. Cannot help you on the solution process. Using Mathematica for the answers and plot generation.
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anonymous
  • anonymous
ok this is the last one, do you think you can help me \[\lim_{x \rightarrow infinity}\sqrt{x^2+3x+1}-x\]
anonymous
  • anonymous
I'll try
anonymous
  • anonymous
\[\text{Limit}\left[\sqrt{x^2+3 x+1}-x,x\to \text{Infinity}\right]=\frac{3}{2}=1.5 \]Refer to the attached plot.
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